A force acts on a $30$gm particle in such a way that the position of the particle as a function of time is given by $x=3t-4t^2+t^3$, where x is in metres and t is in seconds. The work done during the first $4$ second is?

A wheel of radius $1$ meters rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is:

Two SHMs are represented by the equations 
$y1=10sin(3\Omega t+\frac{\Omega }{4})$ and
$y2=5[sin3\Omega t+\sqrt{3}cos 3\Omega t]$. their amplitudes and in the ratio

A simple harmonic oscillator starts from extreme position and covers a displacement half of its amplitude in a time '$t$', the further time taken by it to reach mean position is

The circular motion of a particle whose speed is constant is

Find the distance covered by a particle from time $t=0$ to $t=6\ \sec$. When the particle followsa the movement in straight line according to $y=a\cos \left(\dfrac {\pi}{4}\right)t$:-

The particle executes SHM on a straight line. At two positions its velocity $u$ and $v$ while acceleration, $\alpha$ and $\beta$ respectively $[\beta > \alpha >0]$, the distance between the two positions will be:-

A ball is projected from the ground at angle 0 with the horizontal. After 1 sec it is moving at angle ${ 45 }^{ \circ  }$ with the horizontal and after 2s it is moving horizontally. What is the velocity of projection of the ball ? (Take $g=10\quad { ms }^{ -2 }$)

To understand Simple Harmonic Motion as analogous to circular motion,

The actual distance moved along the circle will be                   the distance moved by the projection on the diameter.

The particle executes SHM on a straight line. At two positions its velocity $u$ and $v$ while acceleration, $\alpha$ and $\beta$ respectively $[\beta > \alpha >0]$, the distance between the two positions will be:-

A stone is projected from the ground with a velocity of $14 \ ms^{-1}$ one second later it clean a wall $2 \ m$ high. The angle of projection is $(g = 10 \ ms^{-2})$ 

The period of a particle it is $8s$. At $t=0$ it is at the mean position. The ratio of the distance covered by the particle in first second and second will be

Sunlight of intensity 1.3 kW m–2 is incident normally on a thin convex lens of focal length 20 cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, kW m–2, at a distance 22 cm from the lens on the other side is _________. 

Simple harmonic motion is the projection of uniform circular motion on the